| 有限群极大子群的θ-子群偶 |
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| 引用本文： | 赵耀庆. 有限群极大子群的θ-子群偶[J]. 数学学报, 1997, 40(1): 67-72. DOI: cnki:ISSN:0583-1431.0.1997-01-008 |
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| 作者姓名： | 赵耀庆 |
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| 作者单位： | 广西大学数学系 南宁530004 |
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| 基金项目： | 国家自然科学基金，广西教委基金 |
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| 摘 要： | N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.
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| 关 键 词： | 有限群 极大子群 极大子群的θ-子群偶 |
| 收稿时间： | 1993-12-10 |
| 修稿时间： | 1996-02-27 |
On Theta Pairs for Maximal Subgroups of Finite Groups |
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| Zhao Yaoqing. On Theta Pairs for Maximal Subgroups of Finite Groups[J]. Acta Mathematica Sinica, 1997, 40(1): 67-72. DOI: cnki:ISSN:0583-1431.0.1997-01-008 |
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| Authors: | Zhao Yaoqing |
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| Affiliation: | Zhao Yaoqing (Department of Mathematics, Guangxi University, Nanning 530004, China) |
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| Abstract: | In the paper "On theta pairs for a maximal subgroup" (Proc. Amer. Math. Soc., V109N3(1990)), N.P. Mukherjee and P.Bhattacharya denned the concept of θ-pairs associated to a maximal subgroup of a finite group, studied the influence of θ-pairs on the structure of the group itself and obtained several results. In this paper we study first the further properties of θ-pairs, then improve in essence some of the main results in Mukherjee and Bhattacharya's paper by using these properties and deal with some new conditions which are necessary and sufficient for a group to be solvable or nilpotent. |
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| Keywords: | Finite groups Maximal subgroups φ-pairs for maximal subgroups |
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